Superharmonic resonance of the quasi-zero-stiffness vibration isolator and its effect on the isolation performance

Quasi-zero-stiffness (QZS) vibration isolator seeks better isolation performance by lowering the natural frequency while maintaining the same static load bearing capacity as equivalent linear isolator. In previous works on QZS isolator, the steady-state response is usually assumed to be a single harmonic at the excitation frequency. However, the QZS isolator can actually exhibit various nonlinear dynamic behaviors such as multi-period responses and chaos. Even the simplest period-1 response, which occurs under most parameter conditions, is not a single harmonic, but contains superharmonics. This paper focuses on the superharmonic resonance that exists in the period-1 response. Both numerical simulation and analytical analysis are conducted; it is shown that there exist multiple superharmonics in the response, the frequencies of which are odd times the excitation frequency, but they are not very apparent when the excitation frequency is higher than a certain value. To characterize the overall properties of these superharmonics, two indices are proposed and analyzed in this paper. In addition, effect of superharmonic resonance on the vibration isolation performance is investigated based on the redefined transmissibility.